Related papers: A combinatorial approach to geometric rough paths …
Many models for complex phenomena use a model for strongly-interacting elements on a small scale to generate larger-scale simulations of some aspects of experimental realizations. These models may be agent-based (as in the case of discrete…
This paper explores a geometric approach to constructing quasi-sure solutions for $G$-stochastic differential equations (G-SDEs) under model uncertainty. We propose a pathwise patching methodology that systematically combines…
This paper explores the Navigation Among Movable Obstacles (NAMO) problem and proposes joint path and push planning: which path to take and in what direction the obstacles should be pushed at, given a start and goal position. We present a…
The majority of extensions to General Relativity display mathematical pathologies (higher derivatives, character change in equations that can be classified within PDE theory, and even unclassifiable ones) that cause severe difficulties to…
In order for automated mobile vehicles to navigate in the real world with minimal collision risks, it is necessary for their planning algorithms to consider uncertainties from measurements and environmental disturbances. In this paper, we…
Based on two isomorphisms of Hopf algebras, we provide a bound in the optimal order on the remainder of the truncated Taylor expansion for controlled differential equations driven by branched rough paths.
We analyze a novel class of rough stochastic control problems that allows for a convenient approach to solving pathwise stochastic control problems with both non-anticipative and anticipative controls. We first establish the well-posedness…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…
Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…
We establish universal approximation theorems for infinite-dimensional geometric rough paths, i.e., we show that continuous functions on the space of infinite-dimensional weakly geometric H\"older continuous rough paths can be approximated…
Multi-dimensional continuous local martingales, enhanced with their stochastic area process, give rise to geometric rough paths with a.s. finite homogenous p-variation, p>2. Here we go one step further and establish quantitative bounds of…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
The class of linear pentapods with a simple singularity variety is obtained by imposing architectural restrictions on the design in such a way that the manipulators singularity variety is linear in orientation position variables. It turns…
Hive plots are a graph visualization style placing vertices on a set of radial axes emanating from a common center and drawing edges as smooth curves connecting their respective endpoints. In previous work on hive plots, assignment to an…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection…